No. You do **not** need custom firmware (CFW) to download and play PSP games legally. The official Sony firmware lets you purchase and download games directly from the PlayStation Store (while it was active) or via Media Go / PC download list.
If you're happy with the official Store library (now mostly inaccessible for new purchases), CFW is unnecessary. If you want to **preserve your UMD collection digitally, run emulators, or access delisted games**, CFW unlocks that—proceed with caution, research your exact model, and back up your NAND.